| | |
| Paragraph 1 |
Whatever problems are proved in more than one figure, if they have
been established in one figure by syllogism, can be reduced
to another
figure, e.g. a negative syllogism in the first figure can be reduced
to the second, and a syllogism in the middle figure to the first,
not all however but some only. |
| Paragraph 2 |
The universal syllogisms in the second figure can be reduced to
the first, but only one of the two particular syllogisms. |
| Paragraph 3 |
But if the syllogism is particular, whenever the negative
statement concerns the major extreme, reduction to the first figure
will be possible, e.g. if A belongs to no B and to some C: |
| Paragraph 4 |
Again syllogisms in the third figure cannot all be
resolved into the
first, though all syllogisms in the first figure can be resolved
into the third. |
| Paragraph 5 |
Of the syllogisms in the last figure one only cannot be resolved
into the first, viz. when the negative statement is not
universal: |
| Paragraph 6 |
It is clear that in order to resolve the figures into one another
the premiss which concerns the minor extreme must be
converted in both
the figures: |
| Paragraph 7 |
One of the syllogisms in the middle figure can, the other
cannot, be
resolved into the third figure. |
| Paragraph 8 |
Syllogisms in the third figure can be resolved into the middle
figure, whenever the negative statement is universal, e.g. if A
belongs to no C, and B to some or all C. |
| Paragraph 9 |
It is clear then that the same syllogisms cannot be resolved in
these figures which could not be resolved into the first figure,
and that when syllogisms are reduced to the first figure these alone are
confirmed by reduction to what is impossible. |
| Paragraph 10 |
It is clear from what we have said how we ought to reduce
syllogisms, and that the figures may be resolved into one another. |
HTML by 
created 1996/11/25 modified 2009/04/26